How can I make scene with multiple gravities going in opposite directions without using a force field?
You can actually achieve this with force fields - providing all your objects have the same mass (or a limited range of masses so that you can have a range of forces - one set for each mass in each direction of simulated "gravity") - similar to the linked answer.

In order for the force to not fall off over distance (so it doesn't ebb away the further away from the force) you need to ensure the falloff power is 0. The strength of the force falls off based on the distance as Force = strength * distance^power (where ^ is 'raised to the power of' - sometimes written as **) - so a power of 0 results in a constant force, irrespective of distance.

For a force that doesn't repel from a single point, use a 'Plane' force - ensuring that the Z direction of the force object is in the desired direction of the force (it can be useful to change the Empty display of the force to 'Arrows' to be able to see the direction of the force 'empty').

Then all that is required is to place the forces and objects on multiple render layers (since forces only affect those objects on their own layer) - so all objects and the associated force that want to experience one 'direction' of gravity on one layer, the next set on another layer, etc.



This can produce the following result :



Note that this is not 'true' gravity as the force experienced by each object will be affected by its mass. To work around this, you can create a separate force per set of masses (so objects with half the mass should be paired with a force of half the strength) - obviously this will only work if you have a very limited set of masses.

Blend file included